I've always loved W.H.D. Rouse's prose translations of Homer. They've been available on Audible for years in an older recording by Nadia May. Blackstone has just reissued them in new readings by Anthony Heald, and they're wonderful. Heald is fast becoming one of my favorite readers. His fast-paced, emotionally-charged style is perfectly suited to the breezy rhythms of Rouse's prose. There are other more poetic translations and readings of The Iliad and The Odyssey, but to my mind these are by far the best prose versions -- especially appropriate if your goal is to be immersed in the story rather than the language.
There are some things about Rouse's style you should be aware of, though. Mostly these are reflections of Homer's style, but some translators smooth it over; Rouse does not. Zeus is sometimes referred to Cronides, Cronion, or just plain God. Other characters are referred to sometimes by their names, sometimes by their patronymics (Agamemnon is Atreides, the son of Atreus; Achilles is Peleides, the son of Peleus). Sometimes, as in Cronides/Cronion, those patronymics have more than one form. In addition, Rouse often uses the word "good" to indicate an in-law relationship: a "good-sister" is actually a sister-in-law; a "good-father" is a father-in-law. To me this is part of the charm of the translation, but if you're not prepared for it, it can be confusing.
The translation by Ian Johnston is immediately accessible without sacrificing the epic forms -- rhythmic metaphors, ritualized repetition, heroic epithets. The reading by Anton Lesser is crisp, clear, and fast-moving. Great job. This being a Naxos audiobook, the only thing missing is music; but once I realized it wasn't there, I didn't miss it: I kept getting caught up in the sweep of the narrative.
This production is based on the Ian Johnston translation and is produced by Yuri Rasovsky. I'm partial to Johnston's work: he also did the outstanding verse translations of Homer recently recorded by Naxos (and available on Audible). This is more than a simple "staged reading." Rasovsky, an old hand at audio theater, pulls out the stops: music and sound effects are used throughout, and I found the choruses, always a dilemma in modern stagings of Greek drama, especially effective. (Oh, and the acting is pretty good too!) Well done, moving, and consistently interesting.